Calculating The Curvature of Spacetime
If you want to calculate what the spacetime curvature is at any point in space, General Relativity allows you to do it, but you need to know a few things.
You need to know the locations, magnitudes and distribution of all the masses in the Universe, just as Newton demanded.
But you also need information about:
how these masses are moving and how they have moved over time, how all other (non-mass) forms of energy are distributed, how the object you are observing or measuring from is moving in a changing Gravitational Field, and how the spatial curvature is changing over time.
Only with those additional pieces of information can you compute how the space is curved for you at a particular location in space and time.
There has to be a cost to this bending and unbending, though.
You can’t just move, say, an accelerating Earth through the Sun’s changing Gravitational Field and not have any consequence.
There is a consequence. Even though it’s small, it can be tested.
Unlike in Newton’s theory, where Earth should trace out a close ellipse as it orbits around the Sun, General Relativity predicts that this ellipse, should precess over time, and that orbit should very slowly decay away.
How long would it take for that to happen?